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CZ:Mathematics Workgroup

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The Citizendium Mathematics Workgroup
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Work plan white paper

The topics below are part of the division of mathematical knowledge to subdisciplines; they come from the 2000 Math. subject classification of the AMS [1] and ZMATH [2], with some minor edits. Each of these top level topics is a big subject, and it is not necessarily our first priority to write a long article on these entries. Our object with outlining this list is to establish a framework. We recommend that when you write a new article, you should try to find a proper node for it. Do not hesitate to put a link for an article you want to work on soon. Feel free to do the same to request a particular important topic to be covered.


  • We kept the original MSC numbering in places.
  • No, of course its not the whole MSC tree - not even close to it. We should eventually put as much of it as appropriate.
  • In some places we really expect some other workgroups (usually the physicists) to do the work alongside - we state where.


  • Do not copy articles from Wikipedia without carefully reading them, verifying both scope and focus. Besides, why not consider writing your article from scratch? Often this permits a better logical structure and more coherence. See CZ:How to convert Wikipedia articles to Citizendium articles
  • Keep in mind three audiences when writing an article: general readers, math students and professionals.

Most wanted math entries

From the encyclopedic point of view, the "high priority" articles are probably listed below at the top level of the tree (or in the table of contents). These are, however, relatively wide syntheses. You may want to start with a bit smaller tasks. A collection of important entries to write (of both types) can be found on the Core Articles page (still to be reviewed and reorganized).

Most popular Wikipedia math entries are: Pi, Mathematics , prime number, computer, trapezoid. These come from the list of 1000 most viewed pages in March 2007.[3] This varies heavily over the time.

On Planet Math, the most popular (as of March 2007) were:[4] circle, proof of Markov's inequality, Cauchy-Schwarz inequality, matrix inverse, Banach fixed point theorem, metric space, invariant subspace, function, manifold, eigenvalue, quartic formula, Jensen's inequality, cross product, real number, differential equation, gradient, natural number, Jacobian matrix, Gram-Schmidt orthogonalization, rational number.


The classification

00-XX General

(for calculus see 26-XX Real functions below)

  • elementary mathematics (pre-university level)
Elementary functions
trigonometric function
point line plane solid stubs
elementary algebra
for suggestions of useful articles to write see also here (pre-calculus or geometry sections)

01-XX History and biography


03-XX Mathematical logic and foundations

Set theory

05-XX Combinatorics

06-XX Order, lattices, ordered algebraic structures

08-XX General algebraic systems

11-XX Number theory

12-XX Field theory and polynomials

  • 12Dxx Real and complex fields
real numbers
complex numbers

13-XX Commutative rings and algebras

14-XX Algebraic geometry

hyperelliptic curve
Kummer surfaces

15-XX Linear and multilinear algebra; matrix theory

16-XX Associative rings and algebras

17-XX Nonassociative rings and algebras

18-XX Category theory; homological algebra

19-XX K-theory

20-XX Group theory and generalizations

  • 20Axx Foundations
  • 20Bxx Permutation groups
  • 20Cxx Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
  • 20Dxx Abstract finite groups
  • 20Exx Structure and classification of infinite or finite groups
  • 20Fxx Special aspects of infinite or finite groups
  • 20Gxx Linear algebraic groups (classical groups) {For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55}
    • 20Hxx Other groups of matrices [See also 15A30]
  • 20Jxx Connections with homological algebra and category theory
  • 20Kxx Abelian groups
  • 20L05 Groupoids (i.e. small categories in which all morphisms are isomorphisms) {For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05}
  • 20Mxx Semigroups
  • 20Nxx Other generalizations of groups
  • 20P05 Probabilistic methods in group theory [See also 60Bxx]*22-XX Topological groups, Lie groups

22-XX Topological groups, Lie groups

For some useful suggestions see: Lie groups topics

26-XX Real functions

Mean value theorem
for some more suggestions of useful articles to write see also list of mathematical topics

28-XX Measure and integration

  • 28Axx Classical measure theory
    • 28A05 Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
    • 28A10 Real- or complex-valued set functions
    • 28A12 Contents, measures, outer measures, capacities
Lebesgue measure
    • 28A15 Abstract differentiation theory, differentiation of set functions [See also 26A24]
    • 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
    • 28A25 Integration with respect to measures and other set functions
Lebesgue integral
Bounded convergence theorem
Monotone convergence theorem
Fatou's lemma
    • 28A33 Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
    • 28A35 Measures and integrals in product spaces
    • 28A50 Integration and disintegration of measures
    • 28A51 Lifting theory [See also 46G15]
    • 28A60 Measures on Boolean rings, measure algebras [See also 54H10]
    • 28A75 Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
    • 28A78 Hausdorff and packing measures
Hausdorff measure
Hausdorff dimension
Packing dimension
    • 28A80 Fractals [See also 37Fxx]
    • 28A99 None of the above, but in this section
  • 28Bxx Set functions, measures and integrals with values in abstract spaces
  • 28Exx Miscellaneous topics in measure theory

30-XX Functions of a complex variable

31-XX Potential theory

  • 31Axx Two-dimensional theory
    • 31A05 Harmonic, subharmonic, superharmonic functions
    • 31A10 Integral representations, integral operators, integral equations methods
    • 31A15 Potentials and capacity, harmonic measure, extremal length [See also 30C85]
    • 31A20 Boundary behavior (theorems of Fatou type, etc.)
    • 31A25 Boundary value and inverse problems
    • 31A30 Biharmonic, polyharmonic functions and equations, Poisson's equation
    • 31A35 Connections with differential equations
    • 31A99 None of the above, but in this section
  • 31Bxx Higher-dimensional theory
    • 31B05 Harmonic, subharmonic, superharmonic functions
    • 31B10 Integral representations, integral operators, integral equations methods
    • 31B15 Potentials and capacities, extremal length
    • 31B20 Boundary value and inverse problems
    • 31B25 Boundary behavior
    • 31B30 Biharmonic and polyharmonic equations and functions
    • 31B35 Connections with differential equations
    • 31B99 None of the above, but in this section
  • 31Cxx Other generalizations
  • 31D05 Axiomatic potential theory

32-XX Several complex variables and analytic spaces

33-XX Special functions

(33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx}

34-XX Ordinary differential equations

see the current article on differential equations

35-XX Partial differential equations

Schrödinger equation

37-XX Dynamical systems and ergodic theory

39-XX Difference and functional equations

40-XX Sequences, series, summability

  • 40Axx Convergence and divergence of infinite limiting processes
  • 40B05 Multiple sequences and series {(should also be assigned at least one other classification number in this section)}
  • 40Cxx General summability methods
  • 40Dxx Direct theorems on summability
  • 40Exx Inversion theorems
  • 40F05 Absolute and strong summability
  • 40Gxx Special methods of summability
  • 40H05 Functional analytic methods in summability
  • 40J05 Summability in abstract structures [See also 43A55, 46A35, 46B15]

41-XX Approximations and expansions

42-XX Fourier analysis

  • 42-04 Explicit machine computation and programs (not the theory of computation or programming)
Fourier series
  • 42Axx Fourier analysis in one variable
  • 42Bxx Fourier analysis in several variables {For automorphic theory, see mainly 11F30}
  • 42Cxx Nontrigonometric Fourier analysis

43-XX Abstract harmonic analysis

44-XX Integral transforms, operational calculus

45-XX Integral equations

46-XX Functional analysis

47-XX Operator theory

49-XX Calculus of variations and optimal control; optimization

51-XX Geometry

for a list of possible suggestions see list of geometry topics

52-XX Convex and discrete geometry

53-XX Differential geometry

54-XX General topology

55-XX Algebraic topology

57-XX Manifolds and cell complexes

58-XX Global analysis, analysis on manifolds

60-XX Probability theory and stochastic processes

  • 60Axx Foundations of probability theory
  • 60Bxx Probability theory on algebraic and topological structures
    • 60C05 Combinatorial probability
    • 60D05 Geometric probability, stochastic geometry, random sets [See also 52A22, 53C65]
  • 60Exx Distribution theory [See also 62Exx, 62Hxx]
  • 60Fxx Limit theorems [See also 28Dxx, 60B12]
  • 60Gxx Stochastic processes
  • 60Hxx Stochastic analysis [See also 58J65]
  • 60Jxx Markov processes
  • 60Kxx Special processes

62-XX Statistics

65-XX Numerical analysis

68-XX Computer science

(do we leave it for the computers Workgorup ?)

70-XX Mechanics of particles and systems

(do we leave it for physics Workgroup??)

74-XX Mechanics of deformable solids

(do we leave it for physics Workgroup??)

76-XX Fluid mechanics

(do we leave it for physics Workgroup??)

78-XX Optics, electromagnetic theory

{For quantum optics, see 81V80} (do we leave it for physics Workgroup??)

80-XX Classical thermodynamics, heat transfer

(do we leave it for physics Workgroup??)

81-XX Quantum theory

82-XX Statistical mechanics, structure of matter

(do we leave it for physics Workgroup??)

83-XX Relativity and gravitational theory

85-XX Astronomy and astrophysics

(do we leave it for physics Workgroup??)

86-XX Geophysics

(do we leave it for physics Workgroup??)

90-XX Operations research, mathematical programming

91-XX Game theory, economics, social and behavioral sciences

(do we leave it for economy Workgroup??)

92-XX Biology and other natural sciences

(do we leave it for biology Workgroup??)

93-XX Systems theory; control


  1. [1]
  2. [2]
  3. [3]
  4. see Planet Math stats page
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